Original Article
Kyungpook Mathematical Journal 2009; 49(4): 605-618
Published online December 23, 2009
Copyright © Kyungpook Mathematical Journal.
A Stage-Structured Predator-Prey System with Time Delay and Beddington-DeAngelis Functional Response
Lingshu Wang1,2, Rui Xu1,3, Guanghui Feng1
1Institute of Applied Mathematics, Shijiazhuang Mechanical Engineering College, Shijiazhuang 050003, P.R. China
2School of Mathematics and Statistics, Hebei University of Economics & Business, Shijiazhuang 050061, P.R. China
3Department of Applied Mathematics, Xi’an Jiaotong University, Xi’an, 710049, P.R. China
A stage-structured predator-prey system with time delay and Beddington-DeAngelis functional response is considered. By analyzing the corresponding characteristic equation, the local stability of a positive equilibrium is investigated. The existence of Hopf bifurcations is established. Formulae are derived to determine the direction of bifurcations and the stability of bifurcating periodic solutions by using the normal form theory and center manifold theorem. Numerical simulations are carried out to illustrate the theoretical results.
Keywords: stability, Hopf bifurcation, predator-prey system, stage structure, time delay, Beddington-DeAngelis functional response